Mr. Musk made the announcement on Monday in a telephone news conference. He said two private individuals approached the company to see if SpaceX would be willing to send them on a weeklong cruise, which would fly past the surface of the moon — but not land — and continue outward before gravity turned the spacecraft around and brought it back to Earth for a landing.

“This would do a long loop around the moon,” Mr. Musk said. The company is aiming to launch this moon mission in late 2018.

The two people would spend about a week inside one of SpaceX’s Dragon 2 capsules, launched on SpaceX’s Falcon Heavy rocket. The spacecraft would be automated, but the travelers would undergo training for emergencies.

Mr. Musk did not say how much the travelers would pay for the ride. “A little bit more than the cost of a crewed mission to the space station would be,” he said.

While the trip appears to be within the technical capabilities of SpaceX, industry experts wondered whether the company could pull it off as quickly as Mr. Musk indicated. “Dates are not SpaceX’s strong suit,” said Mary Lynne Dittmar, executive director of the Coalition for Deep Space Exploration, a space advocacy group consisting of aerospace companies. The Dragon 2 and Falcon Heavy are years behind schedule and have yet to fly.